Question

What mass of a material with density rho is required to make a hollow spherical shell having inner radius r1 and outer radius r2? (Use any variable or symbol stated above as necessary.)'

Answer 1

`m=\rho* (4)/(3) * \pi *(r_2^3-r_1^3 )`

Step-by-step explanation:

• We have to make a hollow sphere of inner radius
  `r_1` and outer radius
  `r_2`.

Then the mass of the material required to make such a sphere would be calculated as:

Total volume of the spherical shell:

`V_t=(4)/(3) \pi.r_2^3`

And the volume of the hollow space in the sphere:

`V_h=(4)/(3) \pi.r_1^3`

Therefore the net volume of material required to make the sphere:

`V=V_t-V_h`

`V=(4)/(3) \pi(r_2^3-r_1^3)`

• Now let the density of the of the material be
  `\rho`.

Then the mass of the material used is:

`m=\rho.V`

`m=\rho* (4)/(3) * \pi *(r_2^3-r_1^3 )`